Pulse butter, cheese, flour, and salt in a food processor until mixture resembles coarse crumbs. Add heavy cream; pulse until just combined. Shape dough into 2 rectangles. Wrap each in plastic. Refrigerate until firm, about 30 minutes.Advertisement
Roll out each rectangle to 1/4 inch thick on a lightly floured surface. Transfer dough to a parchment-lined baking sheet; cut into 1 1/2-inch squares. Separate squares, leaving at least 1/4 inch between them. Chill until firm, about 20 minutes. Using 1-inch cutters, cut out and remove centers of half the squares. Reroll scraps and cut out. Chill until firm, about 20 minutes.
Heat oven to 325 degrees. Bake until pale golden, 18 to 20 minutes. Cool in pan on a rack. Crackers can be kept up to 3 days in an airtight container.
Thin quince paste with the water; heat until warm. Spread 1/2 teaspoon warm paste on the whole crackers, then place cut-out crackers on top.